.. . Annals of Mathematics, 160 (2004), 465–491 Geometry of the uniform spanning forest: Transitions in dimensions 4, 8, 12, By Itai Benjamini, Harry Kesten, Yuval Peres, and Oded Schramm* Abstract The .. . set of edges of a UST on the graph obtained from G by contracting the edges in E1 and deleting the edges in E2 Let H be the graph obtained from Zd by contracting the edges in K1 and deleting the .. . By applying Corollary 3.4 to m + independent copies of the USF relation, and invoking Theorems 4.2 and 4.5 , we infer that a.s., every two vertices in Zd are related by the composition of these...